The local density of dark matter, as suggested by the motion of stars near the sun, is about 1 percent the mass of the sun per cubic parsec, which is about 34.7 cubic light-years. To account for this density with white holes, the scientists calculated that one tiny white hole — much smaller than a proton and about a millionth of a gram, which is equal to about the mass of "half an inch of a human hair," Rovelli said — is needed per 2,400 cubic miles (10,000 cubic kilometers).

These white holes would not emit any radiation, and because they are far smaller than a wavelength of light, they would be invisible. If a proton did happen to impact one of these white holes, the white hole "would simply bounce away," Rovelli said. "They cannot swallow anything." If a black hole were to encounter one of these white holes, the result would be a single larger black hole, he added. As if the idea of invisible, microscopic white holes from the dawn of time were not wild enough, Rovelli and Vidotto further suggested that some white holes in this universe might actually predate the Big Bang. Future research will explore how such white holes from a previous universe might help to explain why time flows only forward in this current universe and not also in reverse, he said.

Rovelli and Vidotto detailed their findings online April 11 in a paper submitted to the Gravity Research Foundation's annual contest for essays on gravitation.